Unit 6 HyperDoc — Expressions (6.EE.A.1–4)

📌 Learning Target

I can…

Write and evaluate numerical expressions using exponents (6.EE.A.1).
Write, read, and evaluate algebraic expressions by substituting values for variables (6.EE.A.2).
Apply the distributive property to generate equivalent expressions (6.EE.A.3).
Identify when two expressions are equivalent (6.EE.A.4).

🔢 Standard: 6.EE.A.1–4 ⏱ Est. time: 45–55 min 📦 Materials: pencil, calculator (optional)

Teacher Notes — Unit 6 (click to expand)

Pacing

Engage 5 min · Explore 10 min · Explain 8 min · Apply 15 min · Reflect 8 min. Total ≈ 46 min. Distributive property questions may need 5 extra minutes for newcomers.

Grouping

Engage — think-pair-share (partners). Explore — pairs on shared device. Apply and Reflect — independent. Compare reflections with a partner before submit.

Differentiation — Support

Provide an order-of-operations anchor chart: Parentheses → Exponents → × ÷ → + −.
For PEMDAS practice, write each step on its own line (scaffold with blanks).
Allow a variable definition card: "variable = unknown number (a letter)".

Differentiation — Challenge

Have students write their own expression, swap with a partner, and evaluate each other's.
Explore: Is 2(x + 3) equivalent to 2x + 6? Prove it with three different values of x.

ESOL / Language Supports

The vocab table in Explain pre-teaches key terms with plain English and examples.
Sentence frames: "The coefficient is ___ because…"; "I evaluated the expression by first ___."
Cognates: expression → expresión, variable → variable, coefficient → coeficiente.
Allow L1 responses for reflections; use a bilingual math dictionary if available.

1 Engage

You have 3 boxes. Each box holds the same number of marbles. You do not know how many! We can call that unknown number b.

Think: How can we write "3 boxes of b marbles" using math?

Do this: Say your idea out loud to a partner. You will check it in Step 4.

2 Explore

Open the tools below to play and explore expressions.

Play the 3D Expression Engine Unit 6 Math Hub Read the Math Novel

Tip: In the game, feed blocks into the machine to build expressions like 3 × b.

3 Explain

Read these key words. Then read the worked examples.

Word	Easy meaning	Example
Expression	Numbers and letters joined by math signs. No equals sign.	3b + 5
Variable	A letter that stands for an unknown number.	b
Coefficient	The number multiplied by a variable.	In 3b, it is 3
Exponent	Small raised number. It tells how many times to multiply the base by itself.	5² = 5 × 5 = 25
Evaluate	Put in a number for the letter and find the value.	If b = 4, then 3b = 12
Distributive	Multiply the outside number by each term inside the parentheses.	2(x + 3) = 2x + 6
Equivalent	Two expressions that always give the same value.	2(x + 3) and 2x + 6

Worked examples

"3 boxes of b marbles" → write as 3b (means 3 × b).
Evaluate: b = 4 → 3b = 3 × 4 = 12.
Exponent: 4³ = 4 × 4 × 4 = 64.
Order of operations: 2 + 3² = 2 + 9 = 11 (exponent first).
Distributive: 3(x + 5) = 3x + 15.

Rule: 3b always means 3 × b. The number in front is the coefficient.

4 Apply — Quick Check

Type your answer in each box. Then press Check My Work.

1. Write "3 boxes of b marbles" as an expression. Use the coefficient and the letter, like 3b.

2. Evaluate 3b when b = 4. Type only the number.

3. Write 5 × 5 × 5 using an exponent. Use the ^ key, like 5^3.

4. In the expression 7m, what is the coefficient? Type only the number.

5. Evaluate 2³ (two to the third power). 2 × 2 × 2. Type only the number.

6. Apply the distributive property: 5(x + 3) = ? Multiply 5 by each term. Write the full expression, e.g. 5x+15.

📊 Rubric

Level	Score	What it looks like
4 — Exceeds	6/6	All expressions, evaluations, and distributive property correct. Reflections use math vocabulary precisely and explain reasoning.
3 — Meets	4–5/6	Correctly writes and evaluates expressions; may make a minor error with exponents or distribution. Reflections are complete.
2 — Approaching	2–3/6	Can identify coefficient and variable but struggles to apply exponents or distributive property. Reflections are brief.
1 — Beginning	0–1/6	Confuses expressions with equations, or cannot yet evaluate by substitution. Needs re-teaching of core concepts.

Answer Key (teacher only)

A1: 3b (also accept "3 × b" or "3*b")
A2: 3 × 4 = 12
A3: 5^3
A4: 7
A5: 2 × 2 × 2 = 8
A6: 5x+15 (also accept "5x + 15")
SC1: b — 9
SC2: b — 13
SC3: b — 2n + 8

5 Reflect

Write 2–4 sentences for each prompt. Use math vocabulary: variable, coefficient, exponent, evaluate, equivalent. Your answers are saved in your PDF/DOC and count toward your grade.

Deliverable: Complete both reflections, press Check My Work above, then submit your PDF or DOC to the class folder.

A. In your own words, what is a variable? Give one example from real life where something is unknown and you would use a variable.

B. What was the trickiest part of this lesson for you — exponents, evaluating, or the distributive property? Explain why it was tricky and what strategy helped you.

When you finish, use Save as PDF or Save as DOC at the top to turn in your work.